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Enlargement: GCSE Maths Definition

Mark Curtis

Written by: Mark Curtis

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2 minutes

Contents

  1. 1. What is an enlargement?
  2. 2. Enlargement revision resources to ace your exams

What is an enlargement?

In GCSE Maths, an enlargement is a transformation that changes the size of a shape. Every enlargement has a scale factor associated with it. A scale factor of 2 means all the side lengths are doubled, a scale factor of 3 means all the side lengths are tripled, etc. Some enlargements produce a shape that is smaller than the original, such as an enlargement with a scale factor of ½ (where the side lengths are halved). In general, if the scale factor is greater than 1, the enlarged shape is bigger, but if the scale factor is less than 1, the enlarged shape is smaller. Every enlargement also has a centre of enlargement, which is the point from which the shape is enlarged. Changing the centre of enlargement will change the position of the enlarged shape.

Graph with shapes on a grid, showing transformations. Shape A is in the top right, shape B is in the bottom left. Red lines converge at a common point.
Shape A is enlarged by a scale factor of 3 about a centre of enlargement at (9, 9) to become shape B.

It is possible for an enlargement to have a negative scale factor. This produces a shape on the opposite side of the centre of enlargement, with the shape rotated by 180°. It helps to imagine lines from the centre of enlargement to the original shape being extended backwards through the centre of enlargement.

Diagram showing a geometric shape 'F' on a grid with lines and points illustrating rotation around the centre of enlargement, marked 'C.o.E.', and new position 'F''.
Shape F is enlarged by a negative scale factor of -⅓ about a centre of enlargement at (6, -1) to become shape F’.

Enlargement revision resources to ace your exams

Enlargements are covered in our revision notes on enlargements from GCSE Maths. You can also have a go at our related exam questions and flashcards on transformations to test your understanding. Don’t forget to check out the past papers for more general exam revision.

Explore GCSE Maths Revision Resources

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Mark Curtis

Author: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

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